• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.773-796
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• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.

• Wind and Structures
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• v.19 no.2
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• pp.219-232
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• 2014

The characteristics of turbulent boundary layers over hilly terrain depend strongly on the hill slope and upstream condition, especially inflow turbulence. Numerical simulations are carried out to investigate the neutrally stratified turbulent boundary layer over two-dimensional hills. Two kinds of hill shape, a steep one with stable separation and a low one without stable separation, two kinds of inflow condition, laminar turbulent, are considered. An auxiliary simulation, based on the local differential quadrature method and recycling technique, is performed to simulate the inflow turbulence be imposed at inlet boundary of the turbulent inflow, which preserves very well in the computational domain. A large separation bubble is established on the leeside of the steep hill with laminar inflow, while reattachment point moves upstream under turbulent inflow condition. There is stable separation on the side of low hill with laminar inflow, whilw not turbulent inflow. Besides increase of turbulence intensity, inflow can efficiently enhance the speedup around hills. So in practice, it is unreasonable to study wind flow over hilly terrain without considering inflow turbulence.

• Computers and Concrete
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• v.25 no.3
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• pp.215-224
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• 2020

In the present study, according to the important of porosity in low specific weight in comparison of high stiffness of carbon nanotubes reinforced composite, buckling and free vibration analysis of sandwich composite beam in two configurations, of laminates using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and three types of porosity distribution on critical buckling load and natural frequency are discussed. It is shown the buckling loads and natural frequencies of laminate 1 are significantly larger than the results of laminate 2. When configuration 2 (the core is made of FRC) and laminate 1 ([0/90/0/45/90]_s) are used, the first natural frequency rises noticeably. It is also demonstrated that the influence of the core height in the case of lower carbon volume fractions is negligible. Even though, when volume fraction of fiber increases, the critical buckling load enhances smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Investigating three porosity patterns, beam with the distribution of porosity Type 2 has the maximum critical buckling load and first natural frequency. Among three elastic foundations (constant, linear and parabolic), buckling load and natural frequency in linear variation has the least amount. For all kind of elastic foundations, when the porosity coefficient increases, critical buckling load and natural frequency decline significantly.

• Advances in nano research
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• v.9 no.4
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• pp.237-250
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• 2020

An accurate plate theory for assessing sandwich structures is of interest in order to provide precise results. Hence, this paper develops Layer-Wise (LW) theory for reaching precise results in terms of buckling and vibration behavior of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) annular nanoplates. Furthermore, for simulating the structure much more realistic, its edges are elastically restrained against in-plane and transverse displacement. The nano structure is integrated with piezoelectric layers. Four distributions of Single-Walled Carbon Nanotubes (SWCNTs) along the thickness direction of the core layer are investigated. The Differential Quadrature Method (DQM) is utilized to solve the motion equations of nano structure subjected to the electric field. The influence of various parameters is depicted on both critical buckling load and frequency of the structure. The accuracy of solution procedure is demonstrated by comparing results with classical edge conditions. The results ascertain that the effects of different distributions of CNTs and their volume fraction are significant on the behavior of the system. Furthermore, the amount of in-plane and transverse spring coefficients plays an important role in the buckling and vibration behavior of the nano-structure and optimization of nano-structure design.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.1-18
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• 2020

Present research is aimed to investigate the free vibration behavior of functionally graded (FG) nanocomposite conical panel reinforced by graphene platelets (GPLs) on the elastic foundation. Winkler-Pasternak elastic foundation surrounds the mentioned shell. For each ply, graphaene platelets are randomly oriented and uniformly dispersed in an isotropic matrix. It is assumed that the Volume fraction of GPLs reainforcement could be different from layer to layer according to a functionally graded pattern. The effective elastic modulus of the conical panel is estimated according to the modified Halpin-Tsai rule in this manuscript. Cone is modeled based on the first order shear deformation theory (FSDT). Hamilton's principle and generalized differential quadrature (GDQ) approach are also used to derive and discrete the equations of motion. Some evaluations are provided to compare the natural frequencies between current study and some experimental and theoretical investigations. After validation of the accuracy of the present formulation and method, natural frequencies and the corresponding mode shapes of FG-GPLRC conical panel are developed for different parameters such as boundary conditions, GPLs volume fraction, types of functionally graded and elastic foundation coefficients.

• Smart Structures and Systems
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• v.26 no.4
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• pp.469-480
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• 2020

This is the first research on the smart control and vibration analysis of a Graphene nanoplatelets (GPLs) Reinforced Composite (GPLRC) porous cylindrical shell covered with piezoelectric layers as sensor and actuator (PLSA) in the framework of numerical based Generalized Differential Quadrature Method (GDQM). The stresses and strains are obtained using the First-order Shear Deformable Theory (FSDT). Rule of the mixture is employed to obtain varying mass density and Poisson's ratio, while the module of elasticity is computed by modified Halpin-Tsai model. The external voltage is applied to sensor layer and a Proportional-Derivative (PD) controller is used for sensor output control. Governing equations and boundary conditions of the GPLRC cylindrical shell are obtained by implementing Hamilton's principle. The results show that PD controller, length to radius ratio (L/R), applied voltage, porosity and weight fraction of GPL have significant influence on the frequency characteristics of a porous GPLRC cylindrical shell. Another important consequence is that at the lower value of the applied voltage, the influence of the smart controller on the frequency of the micro composite shell is much more significant in comparison with the higher ones.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.931-947
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• 2016

The effects of nanotechnology and smartness on the buckling reduction of pipes are the main contributions of present work. For this ends, the pipe is simulated with classical piezoelectric polymeric cylindrical shell reinforced by armchair double walled boron nitride nanotubes (DWBNNTs), The structure is subjected to combined electro-thermo-mechanical loads. The surrounding elastic foundation is modeled with a novel model namely as orthotropic nonhomogeneous Pasternak medium. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite are determined. Employing nonlinear strains-displacements and stress-strain relations as well as the charge equation for coupling of electrical and mechanical fields, the governing equations are derived based on Hamilton's principal. Based on differential quadrature method (DQM), the buckling load of pipe is calculated. The influences of electrical and thermal loads, geometrical parameters of shell, elastic foundation, orientation angle and volume percent of DWBNNTs in polymer are investigated on the buckling of pipe. Results showed that the generated ${\Phi}$ improved sensor and actuator applications in several process industries, because it increases the stability of structure. Furthermore, using nanotechnology in reinforcing the pipe, the buckling load of structure increases.

• Steel and Composite Structures
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• v.19 no.3
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• pp.713-733
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• 2015

In this paper, viscous fluid induced nonlinear free vibration and instability analysis of a functionally graded carbon nanotube-reinforced composite (CNTRC) cylindrical shell integrated with two uniformly distributed piezoelectric layers on the top and bottom surfaces of the cylindrical shell are presented. Single-walled carbon nanotubes (SWCNTs) are selected as reinforcement and effective material properties of FG-CNTRC cylindrical shell are assumed to be graded through the thickness direction and are estimated through the rule of mixture. The elastic foundation is modeled by temperature-dependent orthotropic Pasternak medium. Considering coupling of mechanical and electrical fields, Mindlin shell theory and Hamilton's principle, the motion equations are derived. Nonlinear frequency and critical fluid velocity of sandwich structure are calculated based on differential quadrature method (DQM). The effects of different parameters such as distribution type of SWCNTs, volume fractions of SWCNTs, elastic medium and temperature gradient are discussed on the vibration and instability behavior of the sandwich structure. Results indicate that considering elastic foundation increases frequency and critical fluid velocity of system.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.417-425
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• 2007

The differential quadrature method(DQM) is applied to computation of eigenvalues of the equations of motion governing the free out-of-plane vibration for circular curved beams including the effects of rotatory inertia and transverse shearing deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with exact solutions or numerical solutions by other methods for cases in which they are available. The DQM provides good accuracy even when only a limited number of grid points is used.

• Steel and Composite Structures
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• v.23 no.6
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• pp.691-714
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• 2017

Rotating fluid induced vibration and instability of embedded piezoelectric nano-composite separators subjected to magnetic and electric fields is the main contribution of present work. The separator is modeled with cylindrical shell element and the structural damping effects are considered by Kelvin-Voigt model. Single-walled carbon nanotubes (SWCNTs) are used as reinforcement and effective material properties are obtained by mixture rule. The perturbation velocity potential in conjunction with the linearized Bernoulli formula is used for describing the rotating fluid motion. The orthotropic surrounding elastic medium is considered by spring, damper and shear constants. The governing equations are derived on the bases of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT). The nonlinear frequency and critical angular fluid velocity are calculated by differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the stability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that with increasing volume fraction of SWCNTs, the frequency and critical angular fluid velocity are increased.